On differential equations for the Feynman integral of a one-loop diagram

Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

“…To fix these coefficients, it is necessary to evaluate the Mellin-Barnes integral as a power series solution [24]. In particular, under the condition that the monodromy is irreducible (see 3 Due to the differential relation…”

“…The sunrise or watermelon diagram (see Fig. 1) is one of the simplest Feynman diagrams which have been studied by the physics community as well as by mathematicians over the past fifty years [2][3][4][5][6][7][8][9][10][11][12][13][14]. This diagram has a few different representations.…”

“…1 It could also be rewritten in projective space [2,3]. where F and U are Symanzik polynomials [15] and α = L+1 j=1 α j .…”

On the Regge–Gelfand Problem of Construction of a Pfaff System of Fuchsian Type with a Given Singular Divisor

“…In the paper [3] the Feynman integral of an eigenenergy diagram in a two-dimensional momentum space is investigated. Analogously one can investigate the Feynman integral of a ladder diagram of the sixth order (see [4]) which has the form…”

Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters

“…The strategy of such a kind of analysis is well know in the theory of special functions and the analytical theory of differential equations [12]. As is well known, any Feynman diagram satisfies a system of linear differential or difference equations with polynomial coefficients [13,14,15,16,17]. In modern mathematical language, such a system can be associated with the Gelfand-Karpanov-Zelevinskii functions or D-modules [18].…”